Aptitude Questions on Averages, Mixture and Alligations

Review Averages, Mixture and Alligations concepts

Q. 1 In a lively classroom of five students, the average age is 20 years. One day, a student who is 24 years old leaves the group and is replaced by a new student. Curiously, this change brings down the average age of the group to 19 years. Can you determine the age of the newcomer?

A) 16 years

B) 15 years

C) 14 years

D) 18 years

Check Solution

Ans: D) 18 years

Total age of 5 students initially = $5 \times 20 = 100$

After replacing the student aged 24, total age of 5 students = $5 \times 19 = 95$

Age of the new student = 95−(100−24)=95−76=19

Q. 2 The average of 20 numbers is zero. Out of these, at most, how many numbers can be greater than zero?

A) 19

B) 20

C) 10

D) 1

Check Solution

Ans: A) 19

For the average to be zero, the sum of positive numbers must equal the sum of negative numbers.

So, at most, 19 numbers can be positive if only 1 number is negative to balance their sum.

Q. 3 A farmer has a large pot holding 60 liters of a milk-and-water mixture. Initially, the ratio of milk to water is 2:1. To adjust the composition for his recipe, he adds some water, changing the ratio to 1:2. How much water does the farmer add?

A) 40 l

B) 30 l

C) 20 l

D) 60 l

Check Solution

Ans: A) 40 l

Amount of milk = $\frac{2}{3} \times 60 = 40$
Amount of water = $\frac{1}{3} \times 60 = 20$

Let x liters of water be added to make the ratio 1:2. Then,
$\frac{40}{20 + x} = \frac{1}{2}$

Solving, x=60−20=40

Q. 4 Imagine a cyclist embarking on an adventure! She covers the first half of a certain distance at a steady speed of 30 km/hr and picks up pace in the second half, traveling at 50 km/hr. What would her average speed be for the entire journey?

A) 37.5 km/hr

B) 40 km/hr

C) 45 km/hr

D) 42 km/hr

Check Solution

Ans: A) 37.5 km/hr

Let the total distance be 2D.
Time taken for first half = $\frac{D}{30}$
Time taken for second half = $\frac{D}{50}$

Total time = $150\frac{D}{30} + \frac{D}{50} = \frac{5D + 3D}{150} = \frac{8D}{150}$

Average speed = $\frac{2D}{8D/150} = \frac{2 \times 150}{8} = 37.58$ km/hr

Q. 5 Eight friends decide to track their weight as part of a health challenge. Their average weight increases by 2.5 kg when one of them, who weighs 70 kg, is replaced by a new person. What is the weight of the new person?

A) 90 kg

B) 88 kg

C) 85 kg

D) 80 kg

Check Solution

Ans: A) 90 kg

Increase in total weight = $2.5 \times 8 = 20$ kg
Weight of the new person = 70 + 20 = 90 kg

Q. 6 A mysterious jar holds a mix of two liquids, A and B, in the ratio 4:3. A mischievous scientist removes 10 liters of the mixture and replaces it with pure liquid B. The new ratio becomes 2:3. What is the original volume of the mixture?

A) 35 liters

B) 40 liters

C) 42 liters

D) 45 liters

Check Solution

Ans: A) 35 liters

Let the original quantity of mixture be x liters.

Amount of A = $\frac{4}{7}x$ , Amount of B = $\frac{3}{7}x$

After replacing 10 liters,
New amount of A = $\frac{4}{7}x – \frac{4}{7} \times 10 = \frac{4x – 40}{7}$
New amount of B = $\frac{3}{7}x – \frac{3}{7} \times 10 + 10 = \frac{3x + 40}{7}$

Equating the ratio,
$\frac{\frac{4x – 40}{7}}{\frac{3x + 40}{7}} = \frac{2}{3}$

Solving for x , we get x=35

Q. 7 The average age of a school group of 15 children is 10 years. Soon, they are joined by five younger kids whose average age is 8 years. What becomes the new average age of this group?

A) 9.5 years

B) 9 years

C) 10 years

D) 8.5 years

Check Solution

Ans: A) 9.5 years

Total age of the 15 children = $15 \times 10 = 150$
Total age of the 5 new children = $5 \times 8 = 40$

New total age = 150+40=190
New average age = $9.5\frac{190}{20} = 9.5$ years

Q. 8 Two types of rice are blended to create the perfect mixture for a chef’s special dish. One costs Rs. 60 per kg, and the other costs Rs. 90 per kg. They are mixed in the ratio 2:3. What is the cost per kg of this exquisite mixture?

A) Rs. 75

B) Rs. 80

C) Rs. 78

D) Rs. 85

Check Solution

Ans: A) Rs. 75

Using the alligation rule: Price of mixture=$\frac{2 \times 90 + 3 \times 60}{2 + 3} = \frac{180 + 180}{5} = 75$

Q. 9 A class of 50 students has an average score of 72 in a challenging exam. After removing the scores of the top five performers, the remaining 45 students have an average score of 70. Can you determine the average score of the top five students?

A) 90

B) 82

C) 80

D) 85

Check Solution

Ans: A) 90

Total score of 50 students = $50 \times 72 = 3600$
Total score of remaining 45 students = $45 \times 70 = 3150$
Sum of top 5 scores = 3600 – 3150 = 450

Average score of top 5 students = $\frac{450}{5} = 90$

Q. 10 A barrel contains a flavourful mixture of alcohol and water in the ratio of 3:1. After adding 10 liters of water, the ratio transforms to 2:3. How much alcohol was present in the barrel initially?

A) 6 liters

B) 8 liters

C) 9 liters

D) 10 liters

Check Solution

Ans: C) 9 liters

Let the initial quantity of alcohol be 3x and water x.

After adding 10 liters of water,
New ratio = $\frac{3x}{x + 10} = \frac{2}{3}$

Solving, x=9, so the initial amount of alcohol = $73 \times 9 = 27$

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Aptitude Questions on Averages, Mixture and Alligations

Q. 1 In a lively classroom of five students, the average age is 20 years. One day, a student who is 24 years old leaves the group and is replaced by a new student. Curiously, this change brings down the average age of the group to 19 years. Can you determine the age of the newcomer?

Q. 2 The average of 20 numbers is zero. Out of these, at most, how many numbers can be greater than zero?

Q. 3 A farmer has a large pot holding 60 liters of a milk-and-water mixture. Initially, the ratio of milk to water is 2:1. To adjust the composition for his recipe, he adds some water, changing the ratio to 1:2. How much water does the farmer add?

Q. 4 Imagine a cyclist embarking on an adventure! She covers the first half of a certain distance at a steady speed of 30 km/hr and picks up pace in the second half, traveling at 50 km/hr. What would her average speed be for the entire journey?

Q. 5 Eight friends decide to track their weight as part of a health challenge. Their average weight increases by 2.5 kg when one of them, who weighs 70 kg, is replaced by a new person. What is the weight of the new person?

Q. 6 A mysterious jar holds a mix of two liquids, A and B, in the ratio 4:3. A mischievous scientist removes 10 liters of the mixture and replaces it with pure liquid B. The new ratio becomes 2:3. What is the original volume of the mixture?

Q. 7 The average age of a school group of 15 children is 10 years. Soon, they are joined by five younger kids whose average age is 8 years. What becomes the new average age of this group?

Q. 8 Two types of rice are blended to create the perfect mixture for a chef’s special dish. One costs Rs. 60 per kg, and the other costs Rs. 90 per kg. They are mixed in the ratio 2:3. What is the cost per kg of this exquisite mixture?

Q. 9 A class of 50 students has an average score of 72 in a challenging exam. After removing the scores of the top five performers, the remaining 45 students have an average score of 70. Can you determine the average score of the top five students?

Q. 10 A barrel contains a flavourful mixture of alcohol and water in the ratio of 3:1. After adding 10 liters of water, the ratio transforms to 2:3. How much alcohol was present in the barrel initially?

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